Wild Camping has been banned in Iceland since 2015, please spend the night on a camgound only. Also, the advantage of sleeping in a campground is you a get tons of facilities - restrooms, showers, kitchen etc.
No need to book any site in advance (except groups at some sites)

Here are some of my favorite campgrounds along the ring road.

Expand the Legend on the left for all details

Day 1 Skjol Campground

Price : Adults 1.500 ISK , Children 5-15 years 750 ISK, Senior over 70 years 800 ISK
Showers : 400 ISK per person, Timings - 9:00am to 10:00pm(but were very nice and clean)
Has a restaurant on site 1 June-15 Sept 09:00 - 23:00 15 Sept-1 June 11:00-15:00 and 18:00 - 23:00
Reception for the camping in the restaurant.
Electricity : 1000 ISK per day (17 electric stations on the field for usage)
They have space for 800 campers and caravans The only downside is the restroom area is very small. Restrooms and showers are in separate buildings

There is also another campground nearby - Geysir campsite
Price: Adults-1.800 ISK, Children(8–15yrs)- 500 ISK, Senior citizens/Disabled- 1.000 ISK
Electricity: 900 ISK for 24 hrs
Showers: 500 ISK
Shower timings 8:00 to 11:00 am
Restaurant on site

Day 2 Skogar Campground

Price : 3000 ISK for two people
Showers : 300 ISK per 5 minute
Restroom price included in camping fee, for visitors(non campers) it is 200 kr
Has 3 restaurants on site(Skógar Street Food, Bistro Bar, Center Fossbud Restaurant)
Electricity
It’s just next to Skogafoss, the most iconic waterfall in Iceland. The parking lot is common for both visitors and campers. You need to park your RV or campervan on the gravel
Also, it is always crowded but most of the cars(visitors) leave by 10 pm

The site is awesome, but amenities are not, restrooms were really filthy. I would say not the best site for camping.

Day 3 Þakgil Campground(Thakgil)

Not to be confused with the one at Vik, in fact it is 40 minutes awaya from Vik

Price : 2.000 Isk per person(showers are included in this)
Showers are available round the clock.
Restrooms are extremely clean
Not a crowded campsite
Reception is open until 10:30 pm
There is an awesome picnic area inside a cave and also a small waterfall and creek around the site.

Day 4 Svinafell Campground

Open : 1 May – 30 Sept
Price : 2.000 Isk per person(showers are included in camping fee)
Showers are available round the clock(best thing about this campsite)
Restrooms are extremely clean
Cooking Facility available
Reception is open until 10:30 pm, Kitchen is closed from 12:00 am to 7:00 am
Big dining area
Washing Machine & Dryer available

I’s a gorgeous site, what better can you ask to have stunning glacier views while having your meal. Much better than the Skaftafell campground

Day 5 Hofn campsite

Its just opposite N1 gas station, its usually crowded.
Kitchen area is available from 8:00am to 22:00
Charges 1500 ISK per person plus 300 ISK for 1 tent or car
Showers are not included
Shower charges 50 ISK per minute. You will need coins

Day 6 Fjalladyrd Möðrudalur campground

Price: ISK 1350 per person / Children under 14 years: Free
Showers: ISK 500
Electricity: ISK 800
Restaurant on site (Fjallakaffi)
Cooking and laundry facilities
Use of washing mashine: ISK 500

Okay, so you take showers in the guesthouse on the other side of the campground. I think it was not a guesthouse but somebody’s home, probably the people who worked at the restaurant or on the farm. But can’t complain, it was the by far the best bathroom in Iceland, super clean, warm and big :)
The cooking area was small, unlit and smelly, so we cooked outside.

Day 7 Fosshóll Guesthouse Campground

Price:
Showers:
Electricity:
Restaurant on site. open from 7:30 am until 22:00 pm in high season
Gas Station, Grocery Store

Next to Godafoss waterfall

Day 8 Grundarfjordur Campground

Price : Adults: 1.100 ISK ,Seniors/Disabled: 850 ISK, Free for 16 years and younger
No showers but there is a swimming pool next to the campground
No Kitchen or cooking area
Electricity: 950 ISK

Short drive to Kirkjufell